Modelling of geochemical alteration profiles (e.g., in delta(18)O or Sr-87/Sr-86) resulting from fluid infiltration has provided important constraints on the volumes of fluid that move through the crust during metamorphism. These models consider that alteration results from a combination of advection with diffusion and/or kinetically limited solid-fluid exchange. Models incorporating advection and one of the two broadening mechanisms have analytical solutions, whilst the three-parameter solution does not. Given a particular alteration profile it is, therefore, important from a computational point of view to determine whether use of the more complex three-parameter model places tighter limits on the characteristics of the fluid infiltration event. In this paper we address this problem through modelling of a measured oxygen isotope alteration profile from Naxos, Greece. For each end-member model, we calculate a set of 'best-fit' parameters, emphasising which features of the data control the fit of each of the models. We then consider numerical solutions which allow all three processes to operate, and conduct a grid search in parameter space to map out the structure of the variance between the model and data. While it is not possible to distinguish a single combination of the three processes that produces a strong global minimum in variance, we can distinguish a family of solutions which are equally valid, and we use this 'minimum variance' family to place bounds on the time scales, fluid velocity and porosity characteristic of the fluid alteration event.